Answer :
Sure! Let's break down the solution step by step.
The problem provides the temperature in degrees Fahrenheit and a function to convert this temperature to degrees Celsius. The function used for this conversion is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
where:
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius,
- [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
We are given that the temperature in degrees Fahrenheit is [tex]\( 76.1^\circ F \)[/tex]. We need to determine what [tex]\( C(76.1) \)[/tex] represents.
Step-by-Step Solution:
1. Identify the given temperature in Fahrenheit:
[tex]\[ F = 76.1^\circ F \][/tex]
2. Plug the given temperature into the conversion formula:
[tex]\[ C(76.1) = \frac{5}{9}(76.1 - 32) \][/tex]
3. Perform the subtraction inside the parenthesis first:
[tex]\[ 76.1 - 32 = 44.1 \][/tex]
4. Calculate the value of the fraction:
[tex]\[ \frac{5}{9} \][/tex]
5. Multiply the result from step 3 by the fraction from step 4:
[tex]\[ \frac{5}{9} \times 44.1 \approx 24.5 \][/tex]
So, [tex]\( C(76.1) \approx 24.5^\circ C \)[/tex].
As a result, [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^\circ F \)[/tex] converted to degrees Celsius, which is approximately [tex]\( 24.5^\circ C \)[/tex].
Therefore, the correct answer is:
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
The problem provides the temperature in degrees Fahrenheit and a function to convert this temperature to degrees Celsius. The function used for this conversion is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
where:
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius,
- [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
We are given that the temperature in degrees Fahrenheit is [tex]\( 76.1^\circ F \)[/tex]. We need to determine what [tex]\( C(76.1) \)[/tex] represents.
Step-by-Step Solution:
1. Identify the given temperature in Fahrenheit:
[tex]\[ F = 76.1^\circ F \][/tex]
2. Plug the given temperature into the conversion formula:
[tex]\[ C(76.1) = \frac{5}{9}(76.1 - 32) \][/tex]
3. Perform the subtraction inside the parenthesis first:
[tex]\[ 76.1 - 32 = 44.1 \][/tex]
4. Calculate the value of the fraction:
[tex]\[ \frac{5}{9} \][/tex]
5. Multiply the result from step 3 by the fraction from step 4:
[tex]\[ \frac{5}{9} \times 44.1 \approx 24.5 \][/tex]
So, [tex]\( C(76.1) \approx 24.5^\circ C \)[/tex].
As a result, [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^\circ F \)[/tex] converted to degrees Celsius, which is approximately [tex]\( 24.5^\circ C \)[/tex].
Therefore, the correct answer is:
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
